As we know, SIS problem is defined as: for a function $f_A(s)$=$As$, where $A$ is a fixed, randomly-chosen matrix in $\mathbb{Z}_q^{r \times n}$, it is hard to find elements $s \in \mathbb{Z}_q^{n}$ with some bounded norm $||s||\leq B$ s.t. $f_A(s)$=0 for random $A$.
If I modify the above definition as follows: consider a function $f_A(\{s_i\})$=$\sum_{i=1}^{b} a_iAs_i$, where $a_i \in \mathbb{Z}_q$ are random and $b$ is an integer that is no larger than $|q|$, it is hard to find $\{s_i\} \in (\mathbb{Z}_q^{n})^{b}$ with bounded norm $||s_i||\leq B$ s.t. $f_A(\{s_i\})$=0 for random $A$ as chosen in the original SIS problem. Intuitively there seems to be a connection between these two problems. Can I reduce the hardness of this new problem to that of the aforementioned SIS problem? Thank you in advance.